KATOsuper is an objective‑agnostic framework that accelerates neural topology optimization by coupling neural‑reparameterized TO with a Sensitivity‑Consistent Fourier Neural Operator (SC‑FNO). It uses a forward_split architecture to ensure that sensitivities derived via automatic differentiation remain consistent with predicted objectives, enabling stable optimization. The method demonstrates significant deployment‑time speedups (15–110×) over MATLAB baselines while preserving optimality across 2D and 3D benchmark problems, including compliance and stress minimization, and supports zero‑shot extrapolation to higher resolutions.
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces.
arXiv:2607. 07682v1 Announce Type: new Abstract: The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces.
arXiv:2608. 16080v1 Announce Type: new Abstract: Thermal-aware optimization of multi-die 3D integrated circuits evaluates many designs, each a costly heat-equation solve.
arXiv:2607. 14652v1 Announce Type: new Abstract: Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions.
arXiv:2606. 19921v1 Announce Type: new Abstract: This work proposes an element-based Convolutional Neural Network (CNN) to accelerate density-based Topology Optimization (TO), termed eCNNTO.
arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.
arXiv:2606. 00862v1 Announce Type: cross Abstract: Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for expensive black-box optimization problems.
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.
arXiv:2608. 02036v1 Announce Type: new Abstract: Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, and Newton converges to spurious minima (247% error) even with 1%-accurate field predictions.
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
The paper introduces BOTH, a method that differentiates topology optimization (TO) itself to compute hypergradients for tuning hyperparameters alongside the primary design optimization. By evaluating only one or two TO steps, the approach provides sufficient information and scales to thousands of hyperparameters with a cost comparable to a few standard TO runs. Experiments on stress‑constrained and compliance problems, including a neural‑parameterized density field, demonstrate the effectiveness of this joint optimization strategy.
arXiv:2505. 11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces.